Let ‘PSR’ stand for the principle that whatever is, but need not be, has an explanation for its being.
More exactly:
(PSR) Whatever obtains, but doesn’t obtain of necessity, has an explanation for its obtaining.
Equivalently: Every contingent state of affairs has an explanation.
One might think that PSR has both a priori and empirical support. Regarding the a priori, when we consider an arbitrary state of affairs that obtains but doesn’t have to obtain, we feel motivated to wonder why it obtains; and that wonder seems to reveal an inclination in us to think there ought to be an explanation.
As for empirical support, PSR is a simple (the simplest?) explanation of all the cases of explanation anyone has encountered.
The support is defeated, however, if there are counter-examples to PSR. And, my sense is that most philosophers these days think or suspect or worry that there are counter-examples.
Perhaps the most commonly cited counter-examples are these: (1) quantum events, and (2) the Biggest Contingent Fact. It turns out to be difficult, however, to get these counter-examples to stick, as I’ll attempt to explain. I’ll focus more on (2), since I take it to be the more serious candidate.

First, quantum events. Suppose the link between a complete physical state A and a physical state B is indeterministic. Then we have a violation of PSR only if each of the following are true:
1. The indeterminicy in question is ontological (no hidden variables).
2. There is no non-physical state that, together with A, explains B.
3. There is no indeterministic explanation between A and B.
4. There is no deterministic explanation between tokens of types A and B, despite an indeterminacy at the level of types.
Much could be said about (1) – (4). But here I wish merely to propose that we are not in a position to see that quantum events lack an explanation unless we are in a position to rule out each of (1) – (4). Perhaps there are good reasons to doubt each of (1) – (4), but the task of identifying them is surely not an easy one. (I’m not aware that it’s even been attempted, since I’ve never seen (4) addressed.)
Let’s turn now to the Biggest Contingent Fact, or ‘B’, for short. B is a contingent fact that entails (or includes) all other contingent facts.
Here’s an outline of a standard reason to think that B is a counterexample to PSR:
1. If PSR is true, then B has an explanation.
2. Whatever explains B is either contingent (non-necessary) or necessary.
3. B cannot be explained by something contingent (else circularity).
4. B cannot be explained by something necessary (else B would be necessary).
5. Therefore, B cannot have an explanation. (2,3,4)
6. Therefore, PSR is not true. (1,5)
Consider, first, (3). The motivation for (3) is that you seemingly cannot have circular explanations; for example, no chicken can make itself. Why think a contingent explanation of B would be circular? Presumably because any such explanation would be wholly included in B.
The inference is too quick, however. It could be that the explanation of B is partly contingent and partly necessary, such that the contingent part of the explanation is itself ultimately explained by the necessary part. In that case, there’s no circularity (no fact explains itself). Here’s an illustration. Suppose N is a necessary fact, C1 and C2 are contingent facts, N explains C1, and C1 explains C2. What explains N and C1 and C2? Here’s an answer that avoids circularity: N and C1, which is itself explained by N (or by N’s explaining C1). (This is an example of a fact being explained by a fact it includes, where no circularity results.)
Of course, the above scenario requires that it be possible for a contingent fact to be explained by a necessary fact. That is, it requires the possibility of non-entailing explanations. I’ll discuss this possibility when discussing (4) next.
Consider (4), then. Perhaps the simplest way to motivate (4) is to suppose that every explanation entails it’s explanandum. But why think that? It’s worth pointing out here that I’ve not said anything about the kind of an explanation that PSR calls for. Leibniz says the reason/explanation is “sufficient”. But “sufficient” need not mean logically sufficient (entailing). It could mean adequate, or “satisfying” to those who wondered “why”. Rather than debate over words, let us place no restrictions on the sort of explanation in view.
We normally cite explanations that do not entail their explanandum: for example, I wonder why my son is crying, and I learn it’s because he wanted to eat ice cream for breakfast but wasn’t allowed. Of course, it could be that there are implicit additional facts, such that the cited explanation together with those additional facts would entail the explanandum. But why think that’s actually the case in every case? I propose that filling in the argument here won’t be easy (though I won’t say it can’t be done).
But even if you are convinced that explanations must entail their explanadum, we can work instead with partial explanations. Surely a partial explanation need not entail the thing it merely partially explains. So, when I say ‘explanation’, realize that I mean to include mere partial explanations. (Perhaps we should call the principle, ‘PPR’, the principle of at least partial explanation.)
We might try to motivate (4) by motivating the more specific claim that no necessary fact can explain a contingent fact. But there’s a reason to doubt that claim. The reason is that the necessary fact that a necessarily existing thing wants to create a world with feature phi, is able to do so, and sees that our world would have feature phi would seem to count as a fine explanation of the contingent fact that a necessary being creates our world.
I suggest, then, that (4) is in need of argument, and that it’s not easy to see how to successfully argue for (4). Furthermore, (3) is need of an argument, since it’s not clear that circularity results from its denial. So, it’s not just easy to see that the Biggest Contingent Fact poses a problem for PSR.
Perhaps a better way to argue that B is a counterexample to PSR is to invite candidate explanations of B and show that they fail in one way or another. Here’s a candidate explanation that’s as good as any: B is explained by the fact C that a necessary being choose to bring about certain contingent facts that themselves began a chain of explanations of the rest of the facts that comprise B. But now consider what might explain C? Suppose this: the necessary fact N that a necessary being wanted to bring about a world with feature phi, was able to do so, and saw that bringing about C would be a good way to do so. The problem now is that the fact that N explains C is itself contingent and so needs an explanation, yet whatever explanation we give will imply a further contingent fact in need of an explanation, ad infinitum, and we’ll have no explanation of this entire infinite chain, though it is contingent.
But I’ve got a reply. Why not suppose that N (together with any other relevant necessary truths) provides the ultimate ground, or explanation, of the entire infinite chain of explanations? If that were so, then N would explain (at least partially) each of the following (i) C, (ii) N explains C, (iii) N explains (N explains C), and so on. It’s not clear that there’s a problem here. So, it’s not yet clear that the proposed explanation of B leads to problems.
At this point, someone might worry about the possibility of giving a contrastive explanation: why does N explain this chain rather than some other? But again, I’m placing no requirement on the kind of explanation to be given. Even if there’s no contrastive explanation, we can still suppose that N’s nature provides a (partial) explanation of its activities. That’s not clearly problematic.
What I’ve said here is just an opener. There are other potential counter-examples to consider, and there may be better ways of arguing for the above candidates than the arguments I’ve considered.
What’s become increasingly evident to me, however,–and this is the main point I wish to propose–is that identifying a counter-example to PSR (or to PPR) is no easy task. It might be easier just to believe PSR (or PPR), if indeed it seems evident to you.
I’ll close by floating a hypothesis in support of PSR. The hypothesis is this: one’s basis for thinking of any particular fact that it has an explanation is equally a basis for thinking that contingent facts, in general, have an explanation. Why do I suggest this? Well, suppose you discover milk on your floor. You do not think the milk appeared there with no explanation at all; you think there’s an explanation of the mess. But why? What’s your basis for thinking there’s an explanation here? If PSR is true, then your basis could be this: you realize that the situation didn’t have to obtain, and you instinctively see that whatever obtains, but need not obtain, has an explanation. But suppose that’s not your basis. Then what is it? You might say that you’ve observed events similar to milk spilling that have an explanation. But in what way are they similar? There are infinitely many respects in which the members of the class of events you’ve observed to have an explanation are similar. Which respect is relevant here? If you say all the situations anyone has observed to have an explanation had a beginning and that therefore the milky situation has an explanation on account of its having a beginning, then by the very same reasoning you could also say that all the situations anyone has observed to have an explanation are contingent and that therefore the milky situation has an explanation on account of its being contingent. And then you’d have a basis for PSR. I confess that I don’t see what basis one might have for thinking that spilled milk has an explanation if one doesn’t have an equally good basis for accepting PSR–unless one has good reasons to think there are counterexamples to PSR.

hey joshua!
i don’t understand the dialectic, but reading over the post very quickly, and having taught psr a few times, i had the following (new to me) thought…
some people think modal properties are brute. whether something could have been F is a feature that, if something has it, is not explained by anything else. i think this view is plausible enough. all contingent things have this property: they could have failed to exist. so contingency seems like a good candidate for a property the possession of which needs no explanation.
i then ask myself: what of those things that exist contingently? must there be an explanation for their existence? given that there needn’t be an explanation for why something is contingent, it’s easy (for me) to slide to the claim that there needn’t be an explanation for why a contingent thing exists.
i don’t know the literature. but do you think this move is bad? here’s the move again:
(move) if it’s brute whether something x has the property of contingently existing, then it’s brute whether x, a thing which is contingent, exists.
congrats on the job!!!

Interesting question. I’m not seeing the earlier inference from “modal properties are brute” to “there’s no explanation of there being contingent things”. Suppose x is contingent and has the modal property of ‘could have been F’. If x was caused to exist, should we thereby say that x’s having that modal property was explained? If so, then surely modal properties are not brute. But if we say that modal properties are brute, why couldn’t there be an explanation of there being contingent things without there being an explanation of the modal properties contingent things have? I’m not sure I grasp the inference you have in mind.

Hi Josh,
I remember Trent asking about the PSR on facebook (where serious philosophy gets done!) and I offered two examples that I thought were p.f. plausible counterexamples to PSR. The first is that God chooses freely between two equally attractive options. The second is this. Suppose that the universe’s basic constituents were atom and void. That there is n number of basic constituents seems to be the sort of thing that is contingent but wouldn’t be explained by virtue of anything further. Someone could deny, of course, that there’s such a universe, but I don’t think that sort of response is dialectically effective. Saving the PSR at the expense of a materialist view suggests that the PSR isn’t quite so ontologically neutral as we thought.
Anyway, the big fact. Let’s say p is the big fact, which I take to be something that entails or includes all contingent facts. PSR tells us that there’s some truth of the form:
(i) p because q.
[I can’t quite tell whether PSR tells us that there’s a complete explanation or only a partial one, but I’d read it as complete. Maybe it doesn’t matter for the purposes of this comment, however. Let’s suppose that (i) is true only if q is a complete explanation of p.]
Is (i) contingent? If so, p entails (i) because (i) is included in p. That would seem to conflict with the intuitive idea that a subset of contingent facts included in p cannot be explanatorily prior to p in the way they’d have to be for (i) to be true. If that’s ruled out, then it also seems to rule out that q is contingent. Moreover, it seems to rule out that the relation between p and q holds contingently. So, it seems that neither q nor the explanatory relation between q and p is contingent, in which case p isn’t contingent.
Does this way of putting the argument circumvent your worries about (3) and (4) in your argument?

Feel free to ignore this question as I suspect the answer is familiar to metaphysicians (of which I am not one). Why do we assume that there is a beginning to causal explanations. Example: individual beings are contingent and are members of the set of all human beings that have existed. But why does this set have to have a beginning as far as causal explantions are concerned – why not an infinite regress of explantions (some of which we will never know)? The set of all human beings that have existed is not necessary, but it does exist. Why can’t part of the explantion refer to states that preceded the first truely human being? Evolutionary theory would make this move. If this move is legitimate then it is possible that the chain of explantion goes backwards infinitely, or at least I do not see how one can rule it out. So, my question is, why not a infinite regress of explantions?

Clayton,
Good candidates.that God chooses freely between two equally attractive options
One would need to show that such a fact obtains, or that it obtains if PSR is true. But supposing that can be done, I don’t see why God’s reasons for choosing A could not explain (at least partially) why God chose A, despite God’s having reasons for B, which could have explained his choosing B. We evidently do chose things for reasons, despite possibly choosing something else for other reasons. Perhaps you’ll say that there’s a problem when the options are “equally” attractive–so that one has the same reasons for both options. I’m not sure that’s a problem, but I’m even less sure that that’s a possible situation.a materialistic universe whose basic components are contingent and unexplained
I agree it wouldn’t be dialectically effective to simply deny the possibility of that scenario. But it seems equally ineffective to affirm its possibility. The way I see it, PSR rules out this kind of materialism (though perhaps not all kinds). We can’t say we’ve identified a counterexample to PSR unless/until we provide some good reason to think the counter-example in question obtains or could obtain. (It would be like saying that gravity doesn’t hold for all massive objects on the grounds that there might be some massive objects far away that don’t experience gravity; that’s dialectically ineffective, it seems to me.) (i) q explains B. [I’ll use ‘B’ only because that’s what I originally called the Big Fact]
Your worry is about explanatory priority, since (i) is entailed by B. For maybe 8 years of my life, this very worry prevented me from accepting PSR. But I’ve come to worry that the worry cannot be sustained. It now seems to me that the feeling that there’s a problem here comes from blurring together a kind of inclusion that leads to bad circularity/priority with one that does not. Suppose A causes B, and let N be all the truths about A. Plausibly, N explains B, and N explains (N explains B). But notice that N is both explanatory prior to and included in (entailed by) something that it explains, namely “N explains B”. If there’s no problem here (and I don’t see that there is), why should there be a problem with q being prior to and included in (i)? Maybe there is a problem somewhere; my proposal is that it’s not easy to draw it out successfully (and I don’t know how to do it).
John,
I don’t assume a beginning to causal explanations. (Regarding a contingent causal chain, PRS implies that it’s obtaining will have an explanation–presumably in terms of something non-contingent–whether that chain is finite or infinite.)

i was thinking that psr was not restricted to causal explanations. so, for example, i was thinking that if ned markosian’s “brutal composition” view were true, then psr would be false. there is causal explanation for why some simples get arranged chair-wise, but it’s a brute fact that those simples, so arranged, compose a chair. so there is contingent fact, that the simples compose a chair, and there is no explanation for that fact. in some sense, i suppose, there is a causal explanation for why something has the property being a chair. but in another sense it is a brute fact. i’m thinking that, in this other sense of ‘explanation’ we have a violation of psr. i hope the analogy to the case i described above is obvious enough.

That’s a good clarification, Christian.
In the case of brutal composition, we should distinguish between bruteness at the level of types and bruteness at the level of tokens. It could be that (necessarily) composition occurs any time things are arranged T-wise, such that there’s no explanation as to why things arranged T-wise compose something. That’s not a problem for PSR (because the fact in question is a necessary one). But suppose instead that when particles are arranged T-wise, they can, but need not, compose something. And suppose that there’s no explanation of their composing something if they compose something. This is a very radical scenario: it implies that there could be chairs that flicker in and out of existence a trillion times per second without any explanation. I think PSR probably does rule that out, but I don’t see that as posing a problem for PSR. (The opposite really: It seems that the flicker scenario should be ruled out, but it’s not clear how it can be without PSR.)
(Also, just to be sure: what matters for the PSR I have in mind is not that there be a particular kind of explanation–just that there be some kind or other.)

Hi Joshua,
Let me try to give it another stab. (I’m not convinced that you’re wrong, necessarily, just not sure yet what to think.) Let’s let b be the proposition that expresses the big fact, e be the explanans that explains b, and r be the proposition that b because e.
My worry was more to do with explanatory priority than circularity. If we suppose that r and e are contingent, they are part of b. Intuitively, I thought, that you cannot have a case where some proposition p explains a conjunction, p&q, if the explanans is one of the conjuncts in the explanandum. It’s that that I thought would violate the idea of explanatory priority and I think that that’s what’s happening in our case with b, e, and r. You might resist this, but then it seems that you’re allowing that there are facts that explain themselves, aren’t you? Since e is included in b, I think that you’re committed saying that it’s true that _b&e because e_.
Now, maybe there’s nothing wrong with saying that, but still something bothers me. We’re supposing that r is contingent, so it’s also included in b. Can there be contingent facts that are self-explaining? I think maybe Scotus ran an argument to this effect, which is that if p were truly self-explanatorily true, it wants for nothing outside of it for its truth, in which case there’s nothing a world could lack or have that would be needed for its truth or prevent its truth. If all self-explanatory truths are true necessarily, then it would seem that r is necessary. But, I think r would have to be contingent for reasons sketched in the previous post.
You wrote:
“Suppose A causes B, and let N be all the truths about A. Plausibly, N explains B, and N explains (N explains B). But notice that N is both explanatory prior to and included in (entailed by) something that it explains, namely “N explains B”.”
I only think that this would work if we assumed two things. First, that N includes (as a conjunct?) _B because N_ and B. Second, that conjunctions explain their conjuncts. Maybe worry is with that second assumption and maybe that worry is especially acute in the cases where the explanatory relation between explanans and explanandum holds contingently.
In the example you describe, I take it that it’s plausible that N contains an explanation for B because it contains the fact that A caused B. I don’t see how that bestows any explanatory priority on N. (Indeed, I don’t even see that it shows that _N_ itself is explanatory since containing an explanation and being an explanation don’t seem to be the same thing.) Presumably, “N explains B” is true because N contains “A caused B”, but why would that render N explanatorily prior to B’s explanation? Not quite seeing it yet. I’ll have to mull it over.

i share clayton’s worry, but one response to it is that priority relations are entailing. so if p because q, then necessarily if q then p. this would make the claim necessary, and so it fall outside the scope of psr.
i was thinking of token facts with the composition case. i suppose the flicker scenario is possible if composition is brute. i didn’t have much of a reaction to that consequence. on the other hand, i think composition is necessary. we’re not answering the special composition question by doing empirical science. so i actually don’t think the view is a worry for psr.
i do think which properties are fundamental is likely brute and contingent, as well as which laws of nature hold at our world. perhaps the structure of spacetime is another candidate.
finally, i don’t think we should take necessary truths outside the scope of psr. all sorts of necessary truth have explanations.

Hi Josh,
I’ve been wondering about something like (4) for a bit,
4. B cannot be explained by something necessary (else B would be necessary).
I don’t think that if E explains B and E is necessary, then B is necessary. Tell me what you think. Begin with a toy model with two worlds, w and w’. Let w and w’ be discernible, in particular let w include big contingent fact C and let w’ include big contingent fact C’. Two possible explanations for C and C’, both necessarily true but not entailing that either C or C’ are necessary truths (or necessarily obtain).
Case 1:
1. God utters let it be that C in w.
2. God utters let it be that C’ in w’.
Both (1) and (2) are world-indexed propositions, and so both are necessarily true if true at all. God’s uttering let it be that C in w explains why C obtains in w (similarly for C’ in w’), but it does not entail that C is necessarily true or necessarily obtains (after all C’ is true or obtains in w’). So, not every necessarily true explanation entails a necessarly true explanandum.
Case 2:
1. God causes C to obtain in w and C’ to obtain in w’.
If we have as our explanation the conjunction of evey contingent explanation in each world, our explanation will be necessarily true (even if it is not world-indexed). So, the proposition in (1) explains what C obtins in w and also why C’ obtains in w’. But the explanation in (1) does not itself need explanation, since it is necessarily true. Further, the explanation in (1) does not entail that C necessarily obtains or that C’ does.
This sort of thing (or in the vicinity) seems to solve the problem. And it does not surprse me, since the problem that PvI describes seemed a bit gimmicky to me anyway. Anyway, let me know what you think.

Maybe this can be tightened up a bit as follows, where, as usual, ‘N’ for metaphysical necessity, ‘M’ for metaphysical possibility.
1. N(God utters let it be that C in w only if C is true in w)
2. M~C is also true in w
3. N(God utters let it be that C in w) (world-index prop)
4. M(God does not utter let it be that C) is true in w
5. ~N(God utters let it be that C in w only if NC is true in w).
The downside is that, if C’ holds in w’, then (6) is also true.
6. N(God utters let it be that C in w only if C’ is true in w’).
But that only shows, contrary to assumptions generating the problem, that entailment is not sufficient for explanation.

Let me try something out. Let b be the big fact. There might be a truth q of the form: N willed b’ out of reasons R in favor of willing b’, where b’ is all of b minus q. Let n be: N was impressed by reasons R in favor of willing b’. Suppose n is a necessary truth. Suppose n’ is the correct theory of the nature of explanation. Then n’ is a necessary truth.
For simplicity, suppose n and n’ are each self-explanatory. (I think I might be able to do this without them being self-explanatory, but self-explanatoriness helps here.)
Then:
1. b’ is explained by q
2. q is explained by n.
3. b=b’&q is explained by q&n&n’.
4. That q is explained by n is explained by q&n&n’, where the bulk of the explanatory burden is borne by n’, the theory of explanation which explains why it is that given q and n there is an explanatory connection between them.
5. q&n&n’ is explained by n&n’, because n explains q, n explains n (it’s self-explanatory) and n’ explains n’.
6. That q&n&n’ explains why n explains q is explained by q&n&n’, where the bulk of the explanatory burden is borne by n’ again.
And so on.

Clayton,
Thanks for those helpful comments. I think you very insightly reduce the issue to whether or not it can be the case that p explains p&q (where p is part of the explanandum). I’ve come to think that p explains p&q might be okay in certain cases where p doesn’t need an explanation (or where p entails its own explanation). Let me try to motivate this. Let N be a big necessary fact–a fact that entails all other necessary facts, and suppose N explains c, where c is some contingent fact. Now since c entails N, it’s not implausible that whatever explains c thereby explains c & N. So, it’s not implausible that N explains c & N. In this case, we have an explanation of the form p&q because p, where no contingent fact explains itself, and there’s no priority problem (as far as I see).
(Notice also that whatever might explain N–such as that N is necessary–will be entailed by N itself. So, if N has an explanation, then N plausibly entails [“contains”] its own explanation.)
I suspect the intuition that p explains p & q is bad arises from the ordinary case where p is contingent and in need of an outside explanation. But when p is necessary (or otherwise unexplained), I’m not sure I see a problem. I’m curious what you think about my suggestion that p explains p & q is only problematic in certain (ordinary) cases.
Here’s another thought. Suppose that when p explains q, there’s some proto-explanatory relation E that necessarily holds between p and q (whether p or q obtain or not), such that if p and q both obtain, then p explains q by virtue of the fact that p bears E to q. Then to explain r [b because e], it suffices to explain the conjunction (i) b bears E to e, (ii) e, and (iii) b. Consider, then, the following explanation of each conjunct: (i*) it is necessary that b bears E to e, (ii*) it is necessary that e obtains, and (iii*) e. Here again part of the explandum shows up as part of the explanans, but there’s no circular explanation.
(BTW: in the case where N includes all the truths about A, where A causes B, I had in mind that N includes facts about the nature of A that would explain why A, given that nature, causes B. And then I thought that necessarily, if A causes B, then N explains B, which maybe implies that N explains N’s explaining B in the case where A causes B. I could be wrong about that. And I realize it’s not exactly a case of p explains p & q.)

christian,
I’m curious what you think of my response to Clayton’s worry, in particular to the prospect of having an explanation of the form p&q because p. The response I gave takes me to the edge of my thinking on this topic.i do think which properties are fundamental is likely brute and contingent
I’m curious why you find that likely. It strikes me as more likely that that sort of fact would be necessary (even if PSR turns out false, since for any given contingent fact, I suspect it has an explanation whether or not all contingent facts have an explanation).i don’t think we should take necessary truths outside the scope of psr. all sorts of necessary truth have explanations.
Good point. In restricting psr to contingent facts, I don’t mean to imply that necessary facts don’t have explanations.

Mike,
All that’s very creative. I worry that although we may have an explanation of C if w obtains, we’d not have an explanation of w’s obtaining. But perhaps that’s consistent with your main point.
Alex,
Your suggestion illustrates another way in which you could have an explanation of the form p explains p & q without having a circular explanation (or a priority problem).
You suggest that b’&q is explained by q&n&n’. Here q is part of the explanans and the explanandum. But there’s no circularity because the part of the explanandum that is q is explained by n, and the part of the explanans that is q explains b’. So, q doesn’t explain itself, despite showing up as part of the explanans and explanandum. The example I gave to Clayton (where the big necessary fact N explains a contingent fact c plus whatever c entails) results in a similar situation.
So, it remains unclear to me how to get circularity or priority problems to stick.

Hi Joshua,
Thanks for the response. This isn’t quite my area, but you’re responses have been quite helpful.
“I’m curious what you think about my suggestion that p explains p & q is only problematic in certain (ordinary) cases.”
I think that’s probably fine. My worry was, in part, that a conjunct explaining a conjunction that it’s part of would be problematic when the conjunct was contingent. I might be getting a bit lost in the dialectic, but I thought that b was both contingent and explained by one of its conjuncts. Since that conjunct would be contingent and explain b, the conjunct would be contingent and explain itself (among other things).

My worry was, in part, that a conjunct explaining a conjunction that it’s part of would be problematic when the conjunct was contingent
I was thinking that b’s explanation e could itself be necessary. On the other hand, I do suggest that e may be contingent in my main post (and you suggest the same). So, what do I have to say for myself?
I suggest that there’s still not a problem in the case where e divides into a necessary part and a contingent part, such that the necessary part explains the contingent part (which was actually the suggestion of my main post). To test the plausibility of this, I recommend (to myself and others) thinking about examples that feature such an explanation, such as Alex’s above.
To review, the explanation form in question is this: p&q because p, where p divides into p1 & p2, such that p1 is both necessary and explains p2. (Then the bulk of the explanatory work ultimate rests upon something that’s necessary.)
BTW Clayton, I really appreciate your helping me think this through “out loud”.

I should add that in the above explanation, p explains p&q without thereby explaining each of the conjuncts: i.e. (p1 & p2) explains (p1 & p2 & q), where p1 is necessary and explains p2. Then no contingent fact explains itself.
But now I’m wondering about the nature of the big fact itself. The big fact, b, is a contingent fact that entails all contingent facts. Should we also say that every contingent fact is a conjunct of b? If so, then every conjunction that contains b as a conjunct is also a conjunct of b, which is weird. Worse: the fact R whose conjuncts are all and only facts that are not one of their own conjuncts would be one of its own conjuncts if and only if it is not. To avoid contradiction, we must deny the existence of R. But if there’s no such fact as R, it’s dubious, I think, that there should be any such fact as b, if be is a maximal conjunction. That isn’t to say that there’s no contingent fact that entails all others. It’s just to say that there’s no contingent fact that has all others as conjuncts.
If that’s right, then it will be even harder to generate a circularity/priority problem, I think: (b because e) could be entailed by b without being one of the conjuncts of b–just as (n is necessary) is entailed by n without being one of n’s conjuncts.

Josh:
Yes, the maximal conjunction is problematic. See the Clifton and Davey paper critiquing the Gale-Pruss cosmological argument, and then see Gale and Pruss’s response.
I think it’s all in Religious Studies, late last century.
Gale and Pruss’s response is basically to concede the point that the big conjunction may have some problems, and to suggest that one work with a conjunction of all contingent fundamental propositions or something like that.

Alex,
Yes, I now remember you mentioning this to me (at St. Thomas)– a “mere technical” objection, you suggested. If we go with a conjunction of fundamental propositions, we still won’t have (b because e) as a conjunct of b, especially if e includes facts about b. So, again, it will be more difficulty to motivate a circularity or priority problem, I think.

If PSR is true then there are no random events, because if an event is random then by definition there is no explanation for it. But I see no reason why random events should be impossible, and therefore I believe that they are possible. Thus, if PSR is true then it is not necessary true.
Further I think that PSR is false. Here is why: I have reason to believe that theism is true and therefore that some theodicy holds. All good theodicies I can think of entail that random (and therefore unexplainable) evils obtain. Therefore I have reason to believe that PSR is false.

Thanks for those, Dianelos.I see no reason why random events should be impossible, and therefore I believe that they are possible
Do you mean metaphysically possible? I have no reason to think that the Collatz Conjecture cannot be true. But I also have no reason to think that its denial cannot be true. It would be a mistake to infer that both it and its denial are metaphysically possible, right? More generally, I think we should be careful to distinguish seeing that something is possible from merely failing to see that it isn’t impossible. (So I shouldn’t say, “I see no reason why PSR should be impossible; therefore, I believe it is possibly true.”)
As for theodicy, I want to make sure we distinguish between an event God has no specific reason for allowing from an event that occurs without any explanation. If a bad/evil event occurs, I don’t see why there shouldn’t always be some prior factors that explain (at least indeterministically) that event.

“If PSR is true then there are no random events”
Outcomes of stochastic processes often have perfectly good explanations. It’s not like the casino owner muses: “My incoming is the outcome of a stochastic process. It’s inexplicable that I am making any money.” On the contrary, the casino owner knows exactly why he is making money–he has carefully chosen to include only games where he is likely to do so.
It’s harder to defend the claim that there can be explanations of unlikely outcomes of stochastic processes, but it is probably the predominant view in the philosophy of science that there can.
“All good theodicies I can think of entail that random (and therefore unexplainable) evils obtain.”
That’s not true for the free will based theodicies. It is easy to explain many sins. Why did Eve eat the fruit? Because she wanted to have knowledge (by acquaintance?) of good and evil, and because it looked good to eat.

Joshua,
I meant logically possible. I claim there is a possible world (i.e. a world about which all true propositions entail no logical contradiction) in which random events obtain.
âI think we should be careful to distinguish seeing that something is possible from merely failing to see that it isn’t impossible.â
Right, but as a practical matter (and epistemology is a pragmatical goal-oriented business) I use the principle that unless I have some reason to doubt that X is possible, I take it that it is. I say why worry about impossibility, unless there is some reason for worry? Letâs call that principle âlogical optimismâ. The reason I think that this is a good principle is that it strikes me as plausible that a logical optimist will advance faster than a logical pessimist. For example, in the context of metaphysics the logical optimist will assume that both theism and naturalism are possibly true. In the context of the mind-body problem the logical optimist will assume that the zombie world is possible. And so on. Now in the context of the Collatz conjecture there is reason for worry, for we know of other conjectures that were proven false for very large numbers. So here the logical optimist will not assume logical possibility.
In particular the logical possibility of random phenomena (or, to be precise, phenomena produced by random sources) strikes me as overwhelmingly obvious, and not only because of the absence of defeaters. The whole structure of modern non-classical science is based on the view that virtually all physical phenomena have a random component, and that apparent physical determinism is produced by the addition of a large number of random factors. So, for example, when one lets an apple free in the air it is determined to fall more or less exactly towards the earth in the same sense that when tossing a million coins it is determined that the ratio of heads will be more or less exactly 0.5. Thus randomness appears to be also metaphysically possible, i.e. to perhaps obtain in the actual world.
Incidentally it is not possible to prove the presence of randomness. Even in the easy to think about physical realm it is always possible that the physical universe is executing the fractional expansion of pi after its centillionth bit (which is of course a deterministic process), and whenever we observe an apparently random physical phenomenon (say a photon being detected at the left and not at the right slit) then this is deterministically caused by the next few bits of the expansion.

Alex,
âOutcomes of stochastic processes often have perfectly good explanations.â
Some properties of such outcomes may have good explanations, but not all. In particular the specific value of the outcome of a stochastic process has no explanation. So, for example, one can predict (and explain why) after one tosses a million coins the ratio of heads will most probably fall between 0.49 and 0.51. But one cannot predict (and cannot explain why) one got 500,112 heads.
Randomness is the unpredictable component of a datum. Explanation, in my understanding, is the description of a pattern or order, which entails predictive power. Thus randomness and explanation are mutually exclusive.
But there is perhaps an ambiguity in the concept of âexplanationâ. For example, Keplerâs laws describe an order present in the orbits of the planets, and can therefore be used to predict them. Nevertheless some people would argue that Keplerâs laws do not explain the orbits, because they do not describe the physical mechanism which produces them. In contrast Newtonâs mechanics as well as general relativity do entail a native mechanical model, and are thus said to explain the orbits. On the other hand quantum mechanics does not entail such a model (hence all the trouble with how to interpret QM). Nevertheless I think one should not say that QM does not explain the phenomena it describes.
I believe the confusion arises from the fact that on naturalism the proper explanation of a physical phenomenon is the description of the mechanism that produces it. But theism is not a mechanistic understanding of reality and therefore theists should not restrict the concept of explanation in the way naturalists must.
âWhy did Eve eat the fruit? Because she wanted to have knowledge (by acquaintance?) of good and evil, and because it looked good to eat.â
I donât think that the description of Eveâs character or motivations explain her actual choice. At best, they only explain why Eve would *probably* choose the apple. The actual freedom of a personal choice resides in its unpredictable (and therefore unexplainable) component. Eve was free to not choose the apple, and there is no explanation of why she chose otherwise. Which means that from the outside the free component of choices looks like being produced by a random source. But we who are free persons know that the free component in our choices is not caused randomly, but is caused by the sovereign personal will we possess.
Incidentally I donât think that free will theodicies are viable, for they fail to explain natural evils. In contrast soul-making theodicies appear capable of explaining the existence of natural evils. Here is roughly how it goes: Imagine a world in which moral but no natural evils exist. In such a world the only external source of suffering would be our fellow human beings, and we would therefore tend to put some distance between them and ourselves and choose to live solitary lives â thus missing what is perhaps the principal way for moral advancement, namely our interaction with our fellow imperfect human beings. The actual world we experience does, it seems to me, contain the appropriate balance between moral and natural evil. Namely, there is so much natural evil that we tend to reach for closeness with other human beings, even given the case that they can and often do hurt us. (This rough explanation is incomplete for it does not take into account the existence of natural and moral goods.)

I don’t see why randomness would preclude explanation. Doesn’t “random” just means lacking a specific pattern? Why would a specific pattern be required for an explanation?
Watch this: http://youtu.be/KN-zYxwIimE
The order of the card in this gentleman’s hand is random, but clearly there is an explanation for this order.
Likewise, if we flip a coin any number of times, the number of times it resulted in “head” showing is explained by the ways the coin was flipped.

Dianelos,
Would you find PPR more appealing–the principle that every contingent fact has at least a partial explanation?
Here’s a reason one might think completely unexplained contingent facts are not possible: the simplest explanation as to why there are the (partially) explained contingent facts that there are is that contingent facts must have an explanation (to some extent). This reason could be defeated, of course, if one had an evidently good reason to think that some contingent facts actually lack a (partial) explanation.
Do you think “random” events wouldn’t even have a partial explanation? Can one’s character at least partially explain evil actions?

Dianelos,
“Explanation, in my understanding, is the description of a pattern or order, which entails predictive power.”
I don’t think that’s what explanation is. Bracketing theism, not all patterns are explanatory. Imagine there are a million elephants in the universe, each of which is pink, for no reason at all. There is a pattern there, but it’s not explanatory. It is if anything more mysterious that a million elephants are pink that if one.
But even if explanation is description of a pattern or order, that does not entail that predictions with probability greater than 1/2 can be made. There may be several different ways to continue a sequence, each of the different ways generating a different pattern.
Trivial example: I start with the sequence: 3, 5, 7. What’s next? Well, there are at least two possibilities, each of which produces an elegant pattern. I could put down 9, and then I’ll be listing the odd numbers starting with 3, or I could put down 11, and then I’ll be listing prime numbers starting with 3. If I put down 9, I have a genuine pattern: 3, 5, 7, 9, so by your lights that should be explanatory of the 9. But if I put down 11, I have just as good a pattern, and so that, too, should be explanatory.
Eve was free not to sin, but her sin is explained, though perhaps not predicted with probability greater than a half.

Josh:
For some purposes, it might help to think of explanation modulo necessary truths. I don’t know exactly how to define it, but the thought is something like this: if p&r explains q, where r is necessary, then p explains q modulo necessary truths. If p explains q, and r is necessary, then p explains q&r modulo necessary truths. I don’t know how to generalize from this.
Anyway, a PSR that says that every contingent proposition has an explanation modulo necessary truths might be easier to defend in some ways. Just a hunch.

Dianelos,
“Explanation, in my understanding, is the description of a pattern or order, which entails predictive power.”
I don’t think that’s what explanation is. Bracketing theism, not all patterns are explanatory. Imagine there are a million elephants in the universe, each of which is pink, for no reason at all. There is a pattern there, but it’s not explanatory. It is if anything more mysterious that a million elephants are pink that if one.
But even if explanation is description of a pattern or order, that does not entail that predictions with probability greater than 1/2 can be made. There may be several different ways to continue a sequence, each of the different ways generating a different pattern.
Trivial example: I start with the sequence: 3, 5, 7. What’s next? Well, there are at least two possibilities, each of which produces an elegant pattern. I could put down 9, and then I’ll be listing the odd numbers starting with 3, or I could put down 11, and then I’ll be listing prime numbers starting with 3. If I put down 9, I have a genuine pattern: 3, 5, 7, 9, so by your lights that should be explanatory of the 9. But if I put down 11, I have just as good a pattern, and so that, too, should be explanatory.
Eve was free not to sin, but her sin is explained, though perhaps not predicted with probability greater than a half.

TimHam,
âDoesn’t ârandomâ just means lacking a specific pattern?â
Not quite. For example flipping a coin many times will result in a particular pattern, namely one with approximately the same number of heads and tails. âRamdomâ characterizes a source of data where it is fundamentally impossible (even for a being with infinite cognitive powers) to predict the next datum with better than chance success. (Or, in other words, where the smartest person will not win a betting game against the dumbest person.) If you flip a *random* coin then it is fundamentally impossible to predict whether it will more probably land heads or tails, nor explain why it landed tails when it does so.
âLikewise, if we flip a coin any number of times, the number of times it resulted in âheadâ showing is explained by the ways the coin was flipped.â
If it is thus explained then the throw wasnât really random.

Joshua,
âWould you find PPR more appealing–the principle that every contingent fact has at least a partial explanation?â
If there are random sources in the actual world then there are particular data which are entirely unpredictable and unexplainable, and therefore PPR (the Principle of Partial Reason?) is false. Perhaps one can explain why there are such random sources in the actual world (indeed on theism I think one can) but this does not amount to even a partial explanation of why a particular datum obtains.
Now since I have good reason to believe that theism is true, and further that God would create the world containing random sources, I am inclined to believe that there are random sources in the actual world and therefore that PPR is false also.
Still Iâd like to add that in my judgment the absence of even only partial explanations for minute facts does not make creation a lesser place, but on the contrary makes it more free, more interesting, and in a sense more serious place to be. A micromanaging control-freak-like God strikes me as less than perfect, and a microplanned creation strikes me as lacking respect and consideration for us.
âDo you think ârandomâ events wouldn’t even have a partial explanation?â
If I am right that an explanation (even a partial explanation) entails predictive power, then randomness and explanation are mutually exclusive by definition. (Can you suggest an explanation which does not entail any predictive power whatsoever? Or knowledge which gives you some predictive power but explains nothing?)
âCan one’s character at least partially explain evil actions?â
Yes, of course. So the PPR is true in relation to at least many or most human choices. As well as to many/most physical phenomena. But I think that it is not true as a universal principle.
Actually I think that ultimately there are no reasons or explanations. It may sound shocking at first, especially perhaps to the Western theist, but if we actually consider the matter we see that the core of personal nature (e.g. of our own nature) is not rational. The core of personal nature is the pure, primary, unanalyzable, unexplainable, non-rational will to love. As well as the longing for beauty. There are no reasons for that will and for that longing. Indeed if there were then the reasons one has and not the will and longing one instantiates would be fundamental. That primary will for love and longing for beauty are the reason for many other things, but no other things are the reason for them.

Alex,
âImagine there are a million elephants in the universe, each of which is pink, for no reason at all. There is a pattern there, but it’s not explanatory.â
Strictly speaking, itâs not the pattern itself that is explanatory, but itâs the discovery or the knowledge of that pattern which explains why any elephant I see is pink. (And gives me the power to predict that the next elephant I see will be pink.)
Again, I believe that our concept of âexplanationâ has been contaminated by naturalistic thought patterns according to which the proper form of an explanation is the description of some external causal mechanism. But I donât really need to know the causal mechanisms which make all elephants pink (indeed in your universe no such causes exist) in order to be able to explain the fact that a particular elephant is pink. Nothing causes this elephant to be pink; it is pink because all elephants are.
Incidentally, since in your universe there is no reason at all why all elephants are pink, in your universe PSR is false. (So I take it we agree that PSR is at best contingently true.)
Now letâs consider another universe in which we discover an additional pattern, namely a pattern between the color of the elephants and other facts that hold in that universe. Then we would have found an additional and better explanation of why a particular elephant is pink.
âI start with the sequence: 3, 5, 7. What’s next?â
Right, thatâs a good example, for as you point out there are several patterns that hold for that sequence. Therefore there are also multiple possible explanations for it. Thatâs entirely OK and in fact is often the case in the real world, say in the physical sciences or in criminology. Thatâs why better explanations come with the purposeful search for more data (or experiences). In our case if the next number is not 9 then the explanatory theory that this is the sequence of odd numbers is falsified. And it is not 11 then the explanatory theory that this is the sequence of prime numbers is falsified. But suppose the next number is 11, and the next 13, and the next 17. Now we have more evidence and more confidence that the prime numbers theory is the correct one.
Sometimes there are multiple overlapping patterns that hold for the whole set, albeit one pattern may be more powerful (general, precise) than the other. Consider for example the sequence 1, 2, 4, 5, 9, 12, 22, 33, 55, 90, 143. One correct pattern with some predictive power is that this is a sequence of growing natural numbers. Another correct pattern with much greater predictive power is that this is the Fibonacci sequence within a difference of 1. Now for a real world example consider the set of all known data pertaining to gravitational phenomena. Both Newtonâs mechanics and GR describe patters present, really present, in that data set. So itâs not like GR falsifies or invalidates the reality of Newtonâs laws, or invalidates the explanations for gravitational phenomena given using Newtonâs mechanics. Itâs only physical realists who model physical reality based on the structure of these patterns who had to change their beliefs from Newtonâs model to GRâs model. Which means that, paradoxically, physical realists must be skeptics about physical reality.

I don’t think that “random” is simply another word for “unpredictable”.
Also, flipping a coin many times will PROBABLY result in a pattern with approximately the same number of heads and tails. It’s possible to flip a coin any number of times and never get tials, it just gets more and more unlikely.

Those are good considerations, Dianelos. Thanks for them.
It seems, as you suspected, that we have different notions of ‘explanation’ in mind. You have in mind what I might call ‘epistemic explanation’, whereas I have in mind ‘metaphysical explanation’. The fact that I remember eating breakfast helps me infer (predicts) that I did eat breakfast, but my memory doesn’t metaphysically explain the fact that I ate breakfast. Also: a “random source” could cause an event and so be part of a metaphysical explanation of that event, even if nothing about the source allows us to infer that it was going to cause that particular event.
So, PSR should be read in terms of metaphysical explanations. Do you have a reason to think some contingent facts lack a metaphysical explanation? (We can still have surprise as well as metaphysical indeterminism.)

Dianelos:
“Incidentally, since in your universe there is no reason at all why all elephants are pink, in your universe PSR is false. (So I take it we agree that PSR is at best contingently true.)”
I was describing a universe that I think is impossible but that I expected you to think possible. 🙂

Joshua,
âThe fact that I remember eating breakfast helps me infer (predicts) that I did eat breakfast, but my memory doesn’t metaphysically explain the fact that I ate breakfast.â
Let me first backtrack a little. Clearly it is the case that once one has detected a pattern, one can use it to infer with better than chance success values of any missing part of it. My argument then is that âto explain Xâ is to âto infer X within a particular pattern one has discoveredâ. (One could add that the general explanatory power that comes from discovering a pattern is called âunderstanding.) Now of course what it is one may infer (and explain) depends crucially on the actual pattern. For example, the pattern entailed in our knowledge of flipping coins explains why (and predicts that) the coin will come up either heads or tails, but does not explain why (nor predicts that) the coin has come up heads.
Now in relation to the example you raise, the relevant pattern is the reliability of our memory. This is indeed a fairly stable and general pattern we discover in our experience of life. So, given the presence of one part of the pattern, namely my memory that I ate breakfast this morning, what is the missing part of the pattern I can predict (or explain)? Clearly, as you point out, it cannot be the actual event of my eating breakfast, for my memory of that event does not explain it. I submit that in this case what the reliability-of-memory pattern help one infers (and explain) is that one can safely use the proposition âI ate breakfast this morningâ within some syllogism. In other words the reliability-of-memory pattern has the following general form {I remember X; X has epistemic justification}. Or perhaps simpler {I remember X; X is probably true}
You raise the distinction between epistemic and metaphysical explanations, but surely these are strongly related. After all the presence of metaphysical explanation makes the existence of epistemic explanations possible in the first place. Further, an epistemic explanation is right to the degree it in some sense resembles the metaphysical explanation.
âSo, PSR should be read in terms of *metaphysical* explanations. Do you have a reason to think some contingent facts lack a metaphysical explanation?â
I think the same reason I gave before holds: Given that I have good reason to believe that theism is true, and given that the best theodicies I know of entail random evils (i.e. specific evils for which no metaphysical and hence also no epistemic explanations exist), I have reason to believe that PSR does not hold as a general principle. And in particular that it does not hold for some actual evils (both natural and moral). Actually I am putting this mildly. I believe that the PSR fails all free moral choices, and thus fails quite dramatically in the case of the personal condition.

Alex,
âI was describing a universe that I think is impossible but that I expected you to think possible.â
So what reason do you have for thinking that the universe you described is impossible?
Or for simplicityâs sake letâs take our own universe, the actual world. So imagine that you and an omniscient oracle are taking a stroll near the sea and find two pink pebbles on your path. You ask the oracle what explains the presence of them on your path, and she answers that they were blown in from the nearby beach by a strong wind last night. And then you ask the oracle what explains the fact that both pebbles are pink, and she answers that there is no reason for that; there are pebbles of many different colors on the beach, and it happened just by chance and for no reason at all that the two pebbles blown by the wind were both pink.
Do you see any logical impossibility in the above account? Failing that, do you see any metaphysical impossibility?

Joshua,
I suppose it depends in what sense one uses âpartialâ. In one sense everything that exists has a partial metaphysical explanation, namely that it exists in the world that God saw fit to create.
Let me use a concrete example: A child is killed in an accident. There is a metaphysical explanation (and I think we basically know the epistemic explanation too) of why creation is such that children are killed in accidents. But I think there is no metaphysical explanation (and therefore no epistemic explanation) of why this specific child is killed in that specific accident.
I believe the above very strongly, and not only because it helps one solve the problem from evil. I suggest one can actually see that a world in which a created person suffers a specific natural evil for a specific reason is a world in which that specific evil is justified â and therefore is a world which God would never choose to create. It is *not* the case that there is a reason why that child was killed in that accident. On theism it would be absurd or incoherent if it were.

Dianelos,In one sense everything that exists has a partial metaphysical explanation
If by ‘everything’ you mean all non-necessary things, then it seems we are actually in agreement about PPR (as I’m thinking of it).
The nice thing is that agreement here is perfectly compatible with your insight about specific evils occurring by accident for “no reason”.
I’m assuming that when you say “there is no reason why that child was killed in that accident” that what you say is compatible with saying that there are causal factors that (deterministically or indeterminstically) resulted in the child’s death. Correct me if I’m wrong. If there’s no correction here, then I think we see eye to eye, which is always a pleasure.